HTTPS is HTTP on top of SSL/TLS. That means the entire contents of the HTTP interaction, including the URL, are encrypted. Only network-level information such as the IP address and port of the server is unencrypted. See HTTPS on wikipedia.
However, at the same time, this is only network-level security -- whatever web server is receiving the request will decrypt it (and maybe leave it in logs) before passing it on to any hosted web application. If you choose to use Basic Authentication, HTTPS protects the most obvious concern (sending the password in plaintext), but it has some other issues.
You mention that this is data being exchanged between two systems, which I take to mean that you're implementing the client side of the connection. In that case, regardless of how you send the data (GET/POST/headers/etc.), you need to be extra careful about validating the SSL certificate of the machine you're connecting to. Encrypting the sensitive data doesn't help you at all if a man-in-the-middle can get you to encrypt the data against his keys instead of against the keys of the server you trust. This is a huge source of vulnerabilities.